Graphene, a two-dimensional honeycomb lattice of carbon atoms of great interest in (opto)electronics and plasmonics, can be obtained by means of diverse fabrication techniques, among which chemical vapour deposition (CVD) is one of the most promising for technological applications. The electronic and mechanical properties of CVD-grown graphene depend in large part on the characteristics of the grain boundaries. However, the physical properties of these grain boundaries remain challenging to characterize directly and conveniently. Here we show that it is possible to visualize and investigate the grain boundaries in CVD-grown graphene using an infrared nano-imaging technique. We harness surface plasmons that are reflected and scattered by the graphene grain boundaries, thus causing plasmon interference. By recording and analysing the interference patterns, we can map grain boundaries for a large-area CVD graphene film and probe the electronic properties of individual grain boundaries. Quantitative analysis reveals that grain boundaries form electronic barriers that obstruct both electrical transport and plasmon propagation. The effective width of these barriers (~1020 nm) depends on the electronic screening and is on the order of the Fermi wavelength of graphene. These results uncover a microscopic mechanism that is responsible for the low electron mobility observed in CVD-grown graphene, and suggest the possibility of using electronic barriers to realize tunable plasmon reflectors and phase retarders in future graphene-based plasmonic circuits.